Nuclear dependence of the coherentηphotoproduction reaction in a relativistic approach

Abstract

We study the nuclear (or A) dependence of the coherent η photoproduction reaction in a relativistic impulse approximation approach. We use a standard relativistic parameterization of the elementary amplitude, based on a set of four Lorentz-and gauge-invariant amplitudes, to calculate the coherent production cross section from 4 He, 12 C, and 40 Ca. In contrast to nonrelativistic treatments, our approach maintains the full relativistic structure of the process. The nuclear structure affects the process through the ground-state tensor density. This density is sensitive to relativistic effects and depends on A in a different manner than the vector density used in nonrelativistic approaches. This peculiar dependence results in 4 He having a cross section significantly smaller than that of 12 Cin contrast to existent nonrelativistic calculations. Distortion effects are incorporated through an η-nucleus optical potential that is computed in a simple "tρ" approximation. The nuclear dependence of the coherent η photoproduction process offers a unique opportunity to investigate medium modifications to the elementary γN → ηN amplitude and might help distinguish between different theoretical models that provide an equally good description of the elementary process. In particular, the role played by the background is very significant in spin-isospin saturated nuclei where the dominant resonance S 11 (1535) is suppressed. Furthermore, this reaction contributes significantly to our understanding of nucleon-resonance formation and sheds some light on the propagation of these resonances through the nuclear medium. The A dependence of this reaction is affected by the propagation of the produced η-meson through its interaction with the nucleus. Moreover, the coherent process is sensitive to the whole nuclear volume and, thus, depends on bulk properties of the nucleus. While nonrelativistic treatments suggest that nuclear-structure effects manifest themselves through the conserved vector (or baryon) density [1-3], our recent relativistic analysis suggests that, rather, it is the tensor density that affects the process [4]. This represents an important result, since the tensor density-a quantity as fundamental as the vector density-is not well determined by experiment.An early nonrelativistic study by Bennhold and Tanabe of the coherent η photoproduction process predicted 4 He to have the largest cross section of the three nuclei 4 He, 12 C, and 40 Ca [1]. A recent nonrelativistic study of this process seems to confirm this earlier prediction, although important quantitative differences do emerge [3]. In nonrelativistic treatments the coherent cross section is proportional to the square of the Fourier transform of the vector density. Thus, the particular A dependence predicted by these calculations emerges from a competition between A, which tends to increase the cross section for larger nuclei, and the vector form-factor-which falls rapidly with A. This competition results in 4 He having the largest cross section. Theoretical stud...

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